Assessing renal interstitial fibrosis using compartmental, non-compartmental, and model-free diffusion MRI approaches

Objective To assess renal interstitial fibrosis (IF) using diffusion MRI approaches, and explore whether corticomedullary difference (CMD) of diffusion parameters, combination among MRI parameters, or combination with estimated glomerular filtration rate (eGFR) benefit IF evaluation. Methods Forty-two patients with chronic kidney disease were included, undergoing MRI examinations. MRI parameters from apparent diffusion coefficient (ADC), intra-voxel incoherent motion (IVIM), diffusion kurtosis imaging (DKI), and diffusion-relaxation correlated spectrum imaging (DR-CSI) were obtained both for renal cortex and medulla. CMD of these parameters was calculated. Pathological IF scores (1–3) were obtained by biopsy. Patients were divided into mild (IF = 1, n = 23) and moderate-severe fibrosis (IF = 2–3, n = 19) groups. Group comparisons for MRI parameters were performed. Diagnostic performances were assessed by the receiver operator’s curve analysis for discriminating mild from moderate-severe IF patients. Results Significant inter-group differences existed for cortical ADC, IVIM-D, IVIM-f, DKI-MD, DR-CSI VB, and DR-CSI VC. Significant inter-group differences existed in ΔADC, ΔMD, ΔVB, ΔVC, ΔQB, and ΔQC. Among the cortical MRI parameters, VB displayed the highest AUC = 0.849, while ADC, f, and MD also showed AUC > 0.8. After combining cortical value and CMD, the diagnostic performances of the MRI parameters were slightly improved except for IVIM-D. Combining VB with f brings the best performance (AUC = 0.903) among MRI bi-variant models. A combination of cortical VB, ΔADC, and eGFR brought obvious improvement in diagnostic performance (AUC 0.963 vs 0.879, specificity 0.826 vs 0.896, and sensitivity 1.000 vs 0.842) than eGFR alone. Conclusion Our study shows promising results for the assessment of renal IF using diffusion MRI approaches. Critical relevance statement Our study explores the non-invasive assessment of renal IF, an independent and effective predictor of renal outcomes, by comparing and combining diffusion MRI approaches including compartmental, non-compartmental, and model-free approaches. Key Points Significant difference exists for diffusion parameters between mild and moderate-severe IF. Generally, cortical parameters show better performance than corresponding CMD. Bi-variant model lifts the diagnostic performance for assessing IF. Graphical Abstract


Introduction
Chronic kidney disease (CKD) is a rising public health concern, defined as the loss of renal function for a long period of time [1].The global prevalence of CKD is estimated to be 8-16% [2].A key histological feature of CKD is the presence of interstitial fibrosis (IF) [3], featured by the accumulation of extracellular matrix (ECM) in the renal interstitium and linked to pathologic changes like capillary obliteration and tubular atrophy [2,4,5].Estimated glomerular filtration rate (eGFR) reflects the renal function at a certain time, but is not an independent predictor for renal function impairment.In comparison, IF serves as an independent and effective predictor of renal outcomes [6].Patients with extensive fibrosis are more likely to progress to end-stage renal failure [7,8], and may require planning for dialysis or transplantation.Unfortunately, IF usually progresses silently with no explicit manifestations [9].Biopsy currently remains the only established standard for IF assessment.However, the invasive nature, risk of bleeding, sample bias, and unsuitability for longitude monitoring restrict its clinical value [9].Non-invasive renal IF assessment methods would certainly benefit CKD diagnosis and treatment monitoring, even though they serve a complementary role.
Among various imaging strategies, diffusion-weighted imaging (DWI) and its derivatives stand out for assessing renal microstructure [10][11][12][13].Fibrotic tissues hinder water mobility in extracellular space, which can be captured by DWI.Past research has already linked the apparent diffusion coefficient (ADC) with IF levels and eGFR [12].Moreover, fibrosis-related obstructions like increased collagens would deflect the molecular movement further from the so-called Gaussian diffusion [5].These non-Gaussian properties could be captured not by mono-exponential ADC, but in principle by advanced diffusion models, including compartmental and noncompartmental ones [13].Intra-voxel incoherent motion (IVIM) is a representative of the former, considering both pseudo-and true-diffusion compartments, frequently utilized in studies of renal fibrosis or dysfunction [14][15][16].Decreased IVIM parameters, including D and f, were reported in IF induced by IgA nephritis or unilateral ureteral obstruction [15,16].Conversely, diffusion kurtosis imaging (DKI) represents the non-compartmental model, describing features at high b values by an empirical formula, and was increasingly applied in recent CKD studies [17,18].A negative correlation between renal parenchymal mean diffusivity and a positive correlation between mean kurtosis to histopathological fibrosis score was reported [17].
Despite the promising findings of diffusion models, they heavily rely on artificial constraints, including predetermined components or specific mathematical formulas.Also, these approaches ignore the influence of other properties like relaxation time, limiting their ability to resolve intra-voxel contributions [19].Recent advancements have introduced model-free methods like multi-dimensional correlation magnetic resonance imaging (MRI) [20].A notable example, diffusion-relaxation correlated spectrum imaging (DR-CSI) has preliminarily been applied to kidney evaluation [21,22].Fresh insights were provided by incorporating both the T2 dimension and the peak-based spectrum quantification.
Although the aforementioned methods are all based on diffusion MRI, they are established with different hypotheses, and focus on distinct renal features.Therefore, comparison and combination of them for assessing the pathologic changes could be worthy of attempts.Moreover, their assistance to renal functional biomarkers such as eGFR would also be helpful.Besides, although reports frequently suggest that IF progression correlates with cortical MRI measurement [23,24], some studies also indicate that corticomedullary difference (CMD), like ΔT1 and ΔADC, are effective [3,10,25].Given the assumption that pathologic changes in cortical and medullary microstructure are distinct, it deserves curiosity whether the CMD of these approaches would bring additional interest.
The objective of this study is to (1) assess renal IF using diffusion-based MRI approaches including ADC, IVIM, DKI, and DR-CSI; (2) explore whether CMD of diffusion parameters benefits IF evaluation; and (3) explore whether a combination among these methods or with eGFR could benefit IF evaluation.

Materials and methods
This cross-sectional study is part of an ongoing prospective research plan on characterizing the longitude alterations of pathologic changes in CKD patients using MRI, approved by the Internal Review Board of our hospital.Written informed consent was obtained.

Study subjects
From March 2022 to May 2023, fifty consecutive patients suspected of high risk of CKD (with related clinical symptoms lasting for over 3 months and abnormal blood test results) while meeting the following standard were enrolled and underwent renal MRI: (1) aged 18-80 years; (2) no medical history of renal surgery or other significant intervention; and (3) appropriate for the time-extended MRI, evaluated by the on-site medical staff.In the further analysis, eight patients were excluded due to: (1) unavailable of essential clinical and pathological data (n = 2); (2) finally diagnosed as (or with comorbid) acute renal injury (n = 1); (3) finally diagnosed as end-stage renal disease (stage V) (n = 2); (4) incomplete MRI acquisition (n = 1); and (5) poor MR image quality (n = 2).

Clinical and pathological evaluation
The eGFR was determined using serum creatine based on the CKD epidemiology collaboration formula [26].Renal IF was assessed on a biopsy specimen by the Department of Pathology of our hospital.Percutaneous biopsy was performed within 3 days after the MRI examination, and the specimens were stained using Masson's trichrome method.IF scores were quantified as 1, 2, and 3 based on the percentage of fibrosis < 25%, 25-50%, and > 50%, respectively, according to the Oxford Classification of IgA nephropathy 2016 [27].For further analysis, patients with an IF score of 1 were classified into the "mild IF" group, while patients with IF 2 or 3 were classified into the "moderate-severe IF" group.This grouping criteria is based on two reasons: the worse prognosis for both moderate and severe IF patients compared to mild ones [28], and the relatively small sample size of IF = 3 patients (n = 6).Pathologic diagnosis is given in Table 1.

Image post-processing
Region of interest (ROI) is decided for cortex and medulla separately, including all slices displaying kidney.Two radiologists (with 7 years and 4 years of experience in abdominal MRI, respectively) manually delineated the ROI on DWI b0 with the assistance of T1w images (Fig. S1) by using the segment editor tool embedded in 3D-Slicer (https://www.slicer.org/).Attempts were made to avoid focal areas.An average cortical area of 105.3 cm 2 and medulla area of 37.9 cm 2 were obtained for the 12-b DWI sequence, while an average cortical area of 71.8 cm 2 and medulla area of 26.6 cm 2 were obtained for DR-CSI.ADC mapping was fitted using b0 and b800 images from the 12-b DWI sequence.

IVIM fitting
IVIM and DKI models were fitted voxel-by-voxel using homemade scripts on MATLAB, derived from the 12-b DWI sequence.IVIM model is defined as follows: Where S 0 is the original signal intensity, D and D* are the diffusion coefficients of normal-and pseudo-diffusion components, and f is the pseudo-diffusion fraction.In renal MRI, the selection of the b value may influence the results of diffusion models.Therefore, attempts were made to separate the non-Gaussian effect caused by perfusion and parenchyma.For IVIM analysis, b values utmost to 800 s/mm 2 were selected to avoid the kurtosis effect at high b values.A two-step fitting strategy was applied setting the threshold of 200 s/mm 2 [29].

DKI fitting
DKI model adopted in this study is a direction-averaged model, which is recommended in body MRI [30]: Where MD is the mean diffusivity, and MK is the mean kurtosis.To minimize the potential perfusion effect and concentrate on soft-tissue-induced complexity, b values from 200 s/mm 2 to 2500 s/mm 2 were selected, while low b values were excluded.Similar practices could be found in previous research assuming the large perfusion in the kidney [31].

DR-CSI
The principle of DR-CSI has been illustrated clearly in the literature [20,32].In practice, a discrete form of DR-CSI is adopted: Where f i is spectral intensity representing the distribution on a D-T2 mesh, while each mesh point represents a "component" with specific diffusivity and relaxometry.Specifically, the mesh consists of 30 rows of D (logspaced, 0.3-30 μm 2 /ms) and 30 columns of T2 (logspaced, 5-200 ms).The DR-CSI post-processing workflow is similar to the previous paper [21].Particularly, three compartments A (short T2), B (long T2), and C (high diffusivity) were defined by boundaries manually chosen (T2 boundary within 30-50 ms, diffusivity boundary 6-9 μm 2 /ms) at a visible peak gap.Thus, DR-CSI volume fractions V X for compartment X were obtained by a summation over "components".Compartments A and B were considered to relate to intra-and extra-cellular water, while C was considered to link with microvascular and body liquid flow [21].

CMD
For common MRI parameters, a CMD of a patient was defined as the average value of cortex ROI minus the average value of medullary ROI.The notation "Δ" is used as an abbreviation of CMD before a parameter name (e.g.ΔADC).In addition to traditional DR-CSI CMD (ΔV X ), a novel "spectral CMD" (ΔQ X ) was defined (Fig. 1): a difference-spectrum was obtained by subtracting the normalized medullary D-T2 spectrum from the cortical one, and then filtered by a spectral operator.ΔQ B and ΔQ C were calculated due to the effectiveness of compartments B and C in evaluating IF [21].A detailed description was given in Supplementary Material.

Statistics
All statistical analysis was conducted using SPSS (v23.0;IBM Corp.).The significance criteria were p < 0.05 throughout this study.Intraclass correlation coefficient (ICC) was applied to assess the inter-observer agreement of the MRI parameters.Multivariable linear regression models were established to identify moderate-severe IF from mild IF, including the combination of (1) MRI cortical parameters and corresponding CMD, (2) several MRI parameters, and (3) eGFR and MRI parameters.Several principles were obeyed to choose the appropriate MRI parameter, with details in Supplementary Material ("construction of multivariant models" section).Accordingly, cortical V B , ADC f, and ΔADC were considered in the multi-variant models.The diagnostic performance of parameters (or models) was evaluated using receiver operator's curve (ROC) analysis, with the area under the curve (AUC), sensitivity, and specificity (optimized by Youden's Index) calculated.AUC values < 0.6, 0.6-0.7,0.7-0.8,0.8-0.9, and > 0.9 were interpreted as poor, acceptable, moderate, good, and excellent diagnostic performance.

Clinical characteristics
Finally, data from 42 CKD patients (23 male, 19 female, age 24-74) were adopted into analysis, including 23 mild, 13 moderate, and 6 severe IF patients.Two typical cases are given in Figs. 2 and 3. Detailed clinical information is given in Table 1.No significant differences were found in age (p = 0.726) or sex (p = 0.801) between the mild and

Correlations between MRI parameters and eGFR
The correlations among cortical MRI parameters are presented in Figs. 4 and S2.A strong correlation exists between ADC with MD (r = 0.84, p < 0.001).A moderate correlation exists between MD with D* (r = 0.55), ADC

Assessing IF
The results of ROC analysis are presented in Tables 4 and 5 and Fig. 5. Cortical parameters showed a higher AUC than CMD for all parameters.Among the cortical MRI parameters, DR-CSI V B showed a numerically highest AUC (0.849), while ADC, f, and MD also showed good performance (AUC 0.803-0.838).Among the CMD of parameters, only ΔADC showed good performance (AUC = 0.828).
After combining cortical value with CMD, AUC and specificity for most of the involved parameters were slightly improved (1-5%), except for D. Combining cortical V B with ΔQ B (AUC = 0.879) showed slightly better lift than with ΔV B (AUC = 0.860).The combination of cortical V C with ΔQ C reached a larger sensitivity (0.894) than with ΔV C (0.842), while the AUC is similar (0.806 vs 0.801).
Combining V B with f brings the best performance (AUC = 0.903) among MRI bi-variant models, followed by V B with ΔADC (AUC = 0.897), both bringing a > 5% AUC raise.MRI tri-variant models did not show a large improvement (0.892-0.906).Discriminating moderatesevere IF using eGFR alone turned out a good performance (AUC = 0.879).A combination of cortical V B , ΔADC, and eGFR could reach the excellent performance of AUC 0.963, as well as a rise of specificity (0.826 vs 0.896) and sensitivity (0.842 vs 1.000) compared to eGFR alone.A combination of cortical V B , f, and eGFR also displayed improved AUC (0.879 vs 0.938) and sensitivity (0.842 vs 0.947) compared to eGFR alone.

Discussions
Our study compared, as well as combined several diffusion MRI approaches including conventional (ADC), compartmental (IVIM), non-compartmental (DKI), and model-free (DR-CSI) ones for differentiating CKD patients with moderate or severe IF from those with mild fibrosis.Each method revealed promising imaging biomarkers, demonstrating significant differences between groups.Among them, V B , ADC, ΔADC, f, and MD showed good diagnostic capabilities, which were further enhanced using bi-variant models.Moreover, we found that integrating diffusion MRI metrics offered a diagnostic improvement over using eGFR alone.
Pseudo-diffusion compartments in IVIM are believed to link with perfusion, which is an appealing topic in renal research [14,15,33].For severe CKD patients, tubular atrophy often co-exists with IF, leading to an anticipated reduction in perfusion.This is corroborated by our findings, where f was one-fourth lower in the more severe IF group within both the cortex and medulla.Although cortical D also presented a difference, its diagnostic performance was unexpectedly lower than f, contrary to our initial assumption and previous report in immunoglobulin A nephropathy [16].This discrepancy might be explained by the larger volume of tubular atrophy than interstitium, and is further supported by a stronger correlation for f than D to histopathological fibrosis score in literature [34].A known challenge with IVIM is the instability of D* fitting, evidenced by the substantial standard deviation for D* in this study.Also, D* demonstrates the lowest interobserver agreement, consistent with existing literature [31].Given that common ADC measurement incorporates a low b value (0 s/mm 2 or 50 s/mm 2 ).its correlation to IVIM-f and D* is expected.Among IVIM parameters, our study highlights the clinical relevance of f, followed by D, while D* is not recommended.
While the adoption of DKI in renal studies is increasing, the interpretation of "complexity" remains ambiguous.Contrary to prior research, we did not find a significant change in MK toward severe fibrosis [35].Additionally, the comparative kurtosis between cortex and medulla holds higher, and remains a topic of debate, given contradictions in either fibrotic [35,36] or healthy kidney [31,37,38].Our study reports a slight but positive CMD for both groups of patients.Fortunately, MD is less controversial, as our study demonstrates inter-group differences and good diagnostic performance aligns with the previous findings [35,36].However, its additional value to ADC is limited by their similarity in outcomes, as evidenced by the strong Spearman correlation.This is attributed to their overlapping role in measuring mean diffusivity.The clinical utility of DKI in assessing renal IF may need more investigation.
Advanced compartmental models, such as a threecomponent IVIM model, have been introduced to capture renal microstructure [39].However, accurately determining these compartments is mathematically challenged due to the difficulties of inverting multi-exponential signal decay [40].Encouragingly, this ill-posedness is alleviated by an expanded dimension [19,20], and DR-CSI has showcased its potential in renal microstructure imaging [21].In this study, cortical V B outperformed other parameters, which implies that hindered extra-cellular water may be tightly associated with IF.The newly defined spectral CMD showed promising results, providing the inspiration that model-free approaches may maximize the advantage by leveraging both peak shift and change of fractions.Elevated ΔV B and ΔQ B in moderate-severe IF might relate to the increased ECM accumulation.Decreased ΔV C and ΔQ C hint at a diminished contribution and reduced diffusivity within cortical microvascular.DR-CSI stands out for its less correlation with parameters from other models, likely attributed to the inclusion of T2.This enhanced the diagnostic capability when combining V B with f or ADC.An exception is V C correlated with D*, both representing perfusion-related characters.Nevertheless, inherent negative correlations exist within the DR-CSI fractions since they must add up to 1, underscoring the complexity of interpreting these measurements.
The results of multi-variant models are encouraging, reflecting the diverse biophysical focus of these approaches.Diffusion MRI fulfilled the expectation as a robust adjunct to eGFR, since eGFR could only reflect one, although important, aspect of renal function.Our study reported greater numbers of cortical parameters showing inter-group differences, aligning with the previous opinion that loss of T1w CMD in fibrotic kidneys was raised by cortical changes [25].Yet, a subtraction by medulla is still meaningful, considering the individual variation of kidney ADC [10,41].A trend of CMD towards zero at severe fibrosis was observed, consistent with prior findings on ADC [3,10].As indicated by our findings, the CMD of the advanced diffusion approaches is not a superior indicator on its own but promising as a supplementary input.Combining with kidney segmentation This study has several limitations.First, sampling bias is a challenge, since patients with severe CKD are more likely to be judged as unsuitable for biopsy and therefore not included.This might also explain the relatively smaller sample of severe fibrosis cases (n = 6).Second, the sample size for the three levels of IF is restricted.This also leads to the merging of the moderate and severe IF into one group, which is another limitation in the study design.

Conclusion
In conclusion, our study shows promising results for the assessment of renal IF using diffusion MRI approaches.For most MRI parameters included, significant differences between different IF groups were found in both cortical value and CMD.Several parameters displayed good diagnostic performance discriminating patients with moderate-severe IF from mild ones.Bi-variant MRI model could lift the diagnostic performance.Combining diffusion parameters could bring improvement compared to eGFR alone.These findings could offer insights into noninvasive evaluation strategies for renal pathology.

Fig. 1
Fig. 1 Workflow of the main post-processing procedures.a IVIM and DKI fitting using DWI of different ranges of b value.CMD was obtained for each individual by subtraction of the mean value in cortex and medulla.b DR-CSI post-processing includes two types of CMD.The traditional one simply calculates the volume fraction for the cortex and medulla separately, and performs a subtraction.The new one is obtained by applying a mathematical operator on the cortex-minus-medulla spectrum.c The mathematical operator used in this study.Intensity on the D-T2 spectrum was multiplied by a compartmental filter and order operator, and then summed up.IVIM, intra-voxel incoherent motion; DKI, diffusion kurtosis imaging; DR-CSI, diffusionrelaxation correlated spectrum imaging; ROI, region of interest; MD, mean diffusivity; MK, mean kurtosis

Fig. 5
Fig. 5 ROC curves discriminating moderate-severe fibrosis with (a) cortical DR-CSI parameters and combination to their CMD; b DWI model parameters and combination to their CMD; c multivariant MRI model; d eGFR and combination to MRI parameters.ROC, receiver operator's curve; CMD, corticomedullary difference; DWI, diffusion-weighted imaging; DR-CSI, diffusion-relaxation correlated spectrum imaging; eGFR, estimated glomerular filtration rate; ADC, apparent diffusion coefficient; MD, mean diffusivity

Table 1
Clinical characteristics of the participants in this study CKD chronic kidney disease, IF interstitial fibrosis

Table 2
The detailed MR protocols used in this study TR repetition time, TE echo time, FOV field of view, T1w T1-weighted, T2w T2-weighted, DWI diffusion-weighted imaging, FS fat saturation, TSE turbo spin echo, BLADE proprietary name for periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER), HASTE half-Fourier acquired single-shot turbo spinecho, VIBE volumetric interpolated breath-hold examination moderate-severe IF groups.The moderate-severe IF group had a significantly lower eGFR (51.1 ± 24.7 vs 90.3 ± 19.7, p < 0.001).

Table 3
Group comparison of cortical, medullary values, and CMDs of diffusion MRI-derived parameters Represents the CMD, which was defined as cortical value minus medullary value Significant level: * p < 0.05, ** p < 0.01, *** p < 0.001 IF interstitial fibrosis, ADC apparent diffusion coefficient, IVIM intra-voxel incoherent motion, DKI diffusion kurtosis imaging, MD mean diffusivity, MK mean kurtosis, DR-CSI diffusion relaxation correlated spectrum imaging *Δ techniques, this may bring modest, cost-efficient, enhancement to current CKD assessments.

Table 4
Diagnostic performance of MRI parameters for the discrimination of moderate-severe IF from mild IF Combined linear regression model using cortical value and CMD of MRI parameter Δ Represents the CMD, which was defined as cortical value minus medullary value IF interstitial fibrosis, CMD corticomedullary difference, ADC apparent diffusion coefficient, IVIM intra-voxel incoherent motion, DKI diffusion kurtosis imaging, MD mean diffusivity, MK mean kurtosis, DR-CSI diffusion relaxation correlated spectrum imaging a AUC Cut-off Specificity Sensitivity AUC Cut-off Specificity Sensitivity AUC Cut-off Specificity Sensitivitya

Table 5
Diagnostic performance of multivariant models using MRI, eGFR, and multivariant models combined MRI and eGFR, for the discriminating moderate-severe IF from mild IF MRI parameters in thistable are cortical values if not stated Δ Represents the CMD, which was defined as cortical value minus medullary value IF interstitial fibrosis, ADC apparent diffusion coefficient, eGFR estimated glomerular filtration rate